Please be gentle, first time poster. I have a dwarf lime tree that has, what I think are, spider mites on it that I can't seem to get rid of. I have spot treated with neem oil and insecticidal soap which both appear to cause leaf drop with the soap being more prevalent. I've resorted to using alcohol dipper Q-tips and swabbing areas to try rid the plant of the pests without much luck. The tree seems stressed and is dropping limes when very small along with the flowers. Note: I have it in the house for the winter under a grow lamp by a large window. Any suggestions? The tree is about 5 years old at this time.

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Try giving it a shower once a week. Spider mites hate being washed off. If you can spray underneath the leaves it works even better.

Thank you.

I assume they are spider mites as they make a web. They're very small and off white in color. Too small for my eyes to easily see without magnifying.

Sounds about right. It will take a few sessions in the shower, but you should be able to keep them under control. Just keep a sharp eye out for re-infestations through the winter.